1. Field of the Invention
The present invention relates to frequency band filtering. More specifically, this invention relates to analog as well as digital frequency band filtering wherein the roll-off of the lower pass filter and the rise of the high-pass filter in the vicinity of the crossover frequency are both characterized by high order transform functions that sum to unity, thus resulting in zero phase shift of the recombined signal when the outputs from the low-pass and high-pass filters are recombined together.
2. Description of the Prior Art
It is generally known and an accepted commercial practice to provide a conventional audio hi-fi speaker system consisting, for example, of a tweeter, mid-range and woofer speakers with a crossover circuit or frequency dividing network. Such a crossover circuit traditionally involves at least a low-pass filter, a band-pass filter and a high-pass filter which are designed to receive a signal typically from an amplifier and frequency divide the signal into appropriate bands to drive the corresponding speakers. Conveniently and in particular in the more cost effective popular stereo hi-fi systems, all three speakers and the frequency dividing circuit are incorporated into a single speaker cabinet. In such cases, it is also generally acknowledged that the crossover circuit is a compromise between the desired sharp resolution or separation between frequencies and crossover network induced distortion.
Thus, it is known that at the crossover frequency, the cut-off as a function of frequency should be, in principle, as sharp as possible to minimize the physical distortion associated with the same frequency being reproduced at two different speakers. Consequently, the transfer function characteristic of the filter should be a high order polynomial as a function of frequency (sharp rise and roll-off). However, the use of filters characterized by known higher order transfer functions produce significant phase distortion which in turn is reproduced by the speakers.
Similar dilemmas between the desired sharp delineation between frequency bands and implicit phase distortion associated with known filters with higher order transfer functions that accomplish this sharp cut off are generally found in other essentially real time frequency splitting applications. For example, in such areas as communications, data transmission, seismic prospecting and the like, as well as in digital data processing or the equivalent, similar considerations arise particularly when it is desirable to preserve information within one frequency band separate from the next adjacent band, yet later combine the bands.